Noah Graham's articles on arXiv2019-05-25T00:00:00-04:00http://arxiv.org/a/graham_n_1http://arxiv.org/abs/1810.07671v22019-01-08T08:37:28-05:002018-10-17T13:07:31-04:00Schwarzschild Quantum Fluctuations from Regge-Wheeler ScatteringWe apply a multichannel variable phase method to scattering from Regge-Wheeler potentials. Using a reduced version of the WKB subtraction developed by Candelas and Howard, this approach allows for efficient numerical calculations of scattering data for imaginary wave number, making it possible to compute quantum expectation values in a Schwarzschild curved spacetime background through Wick rotation to the imaginary frequency axis. These scattering theory techniques are also potentially applicable to a variety of other problems involving wave propagation in curved spacetime.Noah Graham10.1103/PhysRevD.99.02500512 pages, 4 .eps figures. v2: fixed typos, added example calculationPhys. Rev. D 99, 025005 (2019)http://arxiv.org/abs/1806.07584v12018-06-20T03:23:17-04:002018-06-20T03:23:17-04:00Vacuum polarization energy of the Shifman-Voloshin solitonWe compute the vacuum polarization energy of soliton configurations in a model with two scalar fields in one space dimension using spectral methods. The second field represents an extension of the conventional $\phi^4$ kink soliton model. We find that the vacuum polarization energy destabilizes the soliton except when the fields have identical masses. In that case the model is equivalent to two independent $\phi^4$ models.H. WeigelN. Graham10.1016/j.physletb.2018.07.027nine papesPhys. Lett. B783 (2018) pp. 434-439http://arxiv.org/abs/1712.04898v22018-03-15T11:45:09-04:002017-12-13T13:08:16-05:00Spectral Methods for Coupled Channels with a Mass GapWe develop a method to compute the vacuum polarization energy for coupled scalar fields with different masses scattering off a background potential in one space dimension. As an example we consider the vacuum polarization energy of a kink-like soliton built from two real scalar fields with different mass parameters.H. WeigelM. QuandtN. Graham10.1103/PhysRevD.97.03601714 pages, 5 figures, matches journal version, references added (surprisingly many)Phys. Rev. D 97, 036017 (2018)http://arxiv.org/abs/1706.07071v12017-06-21T14:08:05-04:002017-06-21T14:08:05-04:00Quantum stabilization of a hedgehog type of cosmic stringWithin a slightly simplified version of the electroweak standard model we investigate the stabilization of cosmic strings by fermion quantum fluctuations. Previous studies of quantum energies considered variants of the Nielsen-Olesen profile embedded in the electroweak gauge group and showed that configurations are favored for which the Higgs vacuum expectation value drops near the string core and the gauge field is suppressed. This work found that the strongest binding was obtained from strings that differ significantly from Nielsen-Olesen configurations, deforming essentially only the Higgs field in order to generate a strong attraction without inducing large gradients. Extending this analysis, we consider the leading quantum correction to the energy per unit length of a hedgehog type string, which, in contrast to the Nielsen-Olesen configuration, contains a pseudoscalar field. To employ the spectral method we develop the scattering and bound state problems for fermions in the background of a hedgehog string. Explicit occupation of bound state levels leads to strings that carry the quantum numbers of the bound fermions. We discuss the parameter space for which stable, hedgehog type cosmic strings emerge and reflect on phenomenological consequences of these findings.M. QuandtN. GrahamH. Weigel10.1016/j.nuclphysb.2017.07.02234 pageshttp://arxiv.org/abs/1606.01090v22016-09-08T13:34:42-04:002016-06-03T09:55:31-04:00Exact Electromagnetic Casimir Energy of a Disk Opposite a PlaneBuilding on work of Meixner [J. Meixner, Z. Naturforschung 3a, 506 (1948)], we show how to compute the exact scattering amplitude (or $T$-matrix) for electromagnetic scattering from a perfectly conducting disk. This calculation is a rare example of a non-diagonal $T$-matrix that can nonetheless be obtained in a semi-analytic form. We then use this result to compute the electromagnetic Casimir interaction energy for a disk opposite a plane, for arbitrary orientation angle of the disk, for separations greater than the disk radius. We find that the proximity force approximation (PFA) significantly overestimates the Casimir energy, both in the case of the ordinary PFA, which applies when the disk is parallel to the plane, and the "edge PFA," which applies when the disk is perpendicular to the plane.Thorsten EmigNoah Graham10.1103/PhysRevA.94.03250913 pages, 4 .eps figures; v2: minor clarifications, expanded discussion in Sec. 4, version accepted for publication in PRAPhys. Rev. A 94, 032509 (2016)http://arxiv.org/abs/1605.09111v22016-08-26T11:02:08-04:002016-05-30T02:11:27-04:00Isospin Invariance and the Vacuum Polarization Energy of Cosmic StringsWe corroborate the previously applied spectral approach to compute the vacuum polarization energy of string configurations in models similar to the standard model of particle physics. The central observation underlying this corroboration is the existence of a particular global isospin transformation of the string configuration. Under this transformation the single particle energies of the quantum fluctuations are invariant, while the inevitable implementation of regularization and renormalization requires operations that are not invariant. We verify numerically that all such variances eventually cancel, and that the vacuum polarization energy obtained in the spectral approach is indeed gauge invariant.H. WeigelM. QuandtN. Graham10.1103/PhysRevD.94.045015matches journal versionPhys. Rev. D 94, 045015 (2016)http://arxiv.org/abs/1411.0734v22014-11-04T20:29:42-05:002014-11-03T18:25:58-05:00Edge Corrections to Electromagnetic Casimir Energies From General-Purpose Mathieu Function RoutinesScattering theory methods make it possible to calculate the Casimir energy of a perfectly conducting elliptic cylinder opposite a perfectly conducting plane in terms of Mathieu functions. In the limit of zero radius, the elliptic cylinder becomes a finite-width strip, which allows for the study of edge effects. However, existing packages for computing Mathieu functions are insufficient for this calculation, because none can compute Mathieu functions of both the first and second kind for complex arguments. To address this shortcoming, we have written a general purpose Mathieu function package, based on algorithms developed by Alhargan [1,2]. We use these routines to find edge corrections to the proximity force approximation for the Casimir energy of a perfectly conducting strip opposite a perfectly conducting plane.Elizabeth Noelle BloseBiswash GhimireNoah GrahamJeremy Stratton-Smith10.1103/PhysRevA.91.0125019 pages, 1 figure; fixed typosPhys. Rev. A 91, 012501 (2015)http://arxiv.org/abs/1407.4642v22014-09-23T08:24:46-04:002014-07-17T07:30:13-04:00Casimir Energies of Periodic Dielectric GratingsReflection of electromagnetic waves from a periodic grating can be described in terms of a discrete coupled multichannel scattering problem. By modeling the grating as a space- and frequency-dependent dielectric, it is possible to use a variable phase method, applied to a generalized Helmholtz equation incorporating both transverse and longitudinal modes, to efficiently compute the scattering $S$-matrix. The projection onto transverse modes of this result, evaluated for imaginary wave vector, provides the information necessary for a Casimir energy calculation. This approach is of particular interest for gratings with deep corrugations, which can limit the applicability of techniques based on the Rayleigh expansion. We demonstrate the method by calculating the Casimir interaction energy between sinusoidal grating profiles as a function of separation and lateral displacement.Noah Graham10.1103/PhysRevA.90.0325076 pages, 2 figures; v2: added clarifications and referencesPhys. Rev. A 90, 032507 (2014)http://arxiv.org/abs/1406.0748v12014-06-03T11:27:25-04:002014-06-03T11:27:25-04:00On the Casimir Energy of Frequency Dependent InteractionsVacuum polarization (or Casimir) energies can be straightforwardly computed from scattering data for static field configurations whose interactions with the fluctuating field are frequency independent. In effective theories, however,such interactions are typically frequency dependent. As a consequence, the relationship between scattering data and the Green's function is modified, which may or may not induce additional contributions to the vacuum polarization energy. We discuss several examples that naturally include frequency dependent interactions: (i) scalar electrodynamics with a static background potential, (ii) an effective theory that emerges from integrating out a heavy degree of freedom, and (iii) quantum electrodynamics coupled to a frequency dependent dielectric material. In the latter case, we argue that introducing dissipation as required by the Kramers-Kronig relations requires the consideration of the Casimir energy within a statistical mechanics formalism, while in the absence of dissipation we can work entirely within field theory, using an alternative formulation of the energy density.N. GrahamM. QuandtH. Weigel10.1103/PhysRevD.90.08500419 pages, 2 figures, 2 tablesPhys. Rev. D 90, 085004 (2014)http://arxiv.org/abs/1401.6225v12014-01-23T19:36:04-05:002014-01-23T19:36:04-05:00Transition To Order After Hilltop InflationWe investigate the rich nonlinear dynamics during the end of hilltop inflation by numerically solving the coupled Klein-Gordon-Friedmann equations in a expanding universe. In particular, we search for coherent, nonperturbative configurations that may emerge due to the combination of nontrivial couplings between the fields and resonant effects from the cosmological expansion. We couple a massless field to the inflaton to investigate its effect on the existence and stability of coherent configurations and the effective equation of state at reheating. For parameters consistent with data from the Planck and WMAP satellites, and for a wide range of couplings between the inflaton and the massless field, we identify a transition from disorder to order characterized by emergent oscillon-like configurations. We verify that these configurations can contribute a maximum of roughly 30% of the energy density in the universe. At late times their contribution to the energy density drops to about 3%, but they remain long-lived on cosmological time-scales, being stable throughout our simulations. Cosmological oscillon emergence is described using a new measure of order in field theory known as relative configurational entropy.Marcelo GleiserNoah Graham10.1103/PhysRevD.89.08350210 pages, 6 figures totaling 25 .eps filesPhys. Rev. D 89, 083502 (2014)http://arxiv.org/abs/1310.7878v12013-10-29T13:03:42-04:002013-10-29T13:03:42-04:00Radiatively induced symmetry breaking and the conformally coupled magnetic monopole in AdS spaceWe implement quantum corrections for a magnetic monopole in a classically conformally invariant theory containing gravity. This yields the trace (conformal) anomaly and introduces a length scale in a natural fashion via the process of renormalization. We evaluate the one-loop effective potential and extract the vacuum expectation value (VEV) from it; spontaneous symmetry breaking is radiatively induced. The VEV is set at the renormalization scale $M$ and we exchange the dimensionless scalar coupling constant for the dimensionful VEV via dimensional transmutation. The asymptotic (background) spacetime is anti-de Sitter (AdS) and its Ricci scalar is determined entirely by the VEV. We obtain analytical asymptotic solutions to the coupled set of equations governing gravitational, gauge and scalar fields that yield the magnetic monopole in an AdS spacetime.Ariel EderyNoah Graham10.1007/JHEP11(2013)10918 pages, one figure, to appear in JHEPhttp://arxiv.org/abs/1305.5144v22013-09-25T14:40:30-04:002013-05-22T10:17:37-04:00Attractive Electromagnetic Casimir Stress on a Spherical Dielectric ShellBased on calculations involving an idealized boundary condition, it has long been assumed that the stress on a spherical conducting shell is repulsive. We use the more realistic case of a Drude dielectric to show that the stress is attractive, matching the generic behavior of Casimir forces in electromagnetism. We trace the discrepancy between these two cases to interactions between the electromagnetic quantum fluctuations and the dielectric material.N. GrahamM. QuandtH. Weigel10.1016/j.physletb.2013.09.025Five pages, one figure, pdflatex, matches version to be pusblished in Phys Lett BPhys. Lett. B726 (2013) 846http://arxiv.org/abs/1303.6354v12013-03-25T20:30:58-04:002013-03-25T20:30:58-04:00Electromagnetic Casimir Forces in Elliptic Cylinder GeometriesThe scattering theory approach makes it possible to carry out exact calculations of Casimir energies in any geometry for which the scattering T-matrix and a partial wave expansion of the free Green's function are available. We implement this program for the case of a perfectly conducting elliptic cylinder, thereby completing the set of geometries where electromagnetic scattering is separable. Particular emphasis is placed on the case of zero radius, where the elliptic cylinder reduces to a strip.Noah Graham10.1103/PhysRevD.87.1050047 pages, 3 .eps figuresPhys. Rev. D 87, 105004 (2013)http://arxiv.org/abs/1303.0178v22013-03-15T07:20:07-04:002013-03-01T09:34:28-05:00Quantum Stabilization of a Closed Nielsen-Olesen StringWe revisit the classical instability of closed strings in the Abelian Higgs model. The instability is expressed by a vanishing energy as the torus-like configuration shrinks to zero size. We treat the radius of the torus as a collective coordinate and demonstrate that a quantum mechanical treatment of this coordinate leads to a stabilization of the closed string at small radii.M. QuandtN. GrahamH. Weigel10.1103/PhysRevD.87.08501323 pages, pdflatex, version to be published in Phys Rev DPhys. Rev. D87 (2013) 085013http://arxiv.org/abs/1210.0777v22012-12-23T13:40:39-05:002012-10-02T09:58:20-04:00Variable Phase S-Matrix Calculations for Asymmetric Potentials and DielectricsMotivated by recently developed techniques making it possible to compute Casimir energies for any object whose scattering S-matrix (or, equivalently, T-matrix) is available, we develop a variable phase method to compute the S-matrix for localized but asymmetric sources. Starting from the case of scalar potential scattering, we develop a combined inward/outward integration algorithm that is numerically efficient and extends robustly to imaginary wave number. We then extend these results to electromagnetic scattering from a position-dependent dielectric. This case requires additional modifications to disentangle the transverse and longitudinal modes.Aden ForrowNoah Graham10.1103/PhysRevA.86.06271512 pages, 5 .eps figures, RevTeX; v2: added sample numerical calculations, minor correctionsPhys. Rev. A 86, 062715 (2012)http://arxiv.org/abs/1105.1112v22011-06-10T12:25:50-04:002011-05-05T12:08:07-04:00Fermion Energies in the Background of a Cosmic StringWe provide a thorough exposition, including technical and numerical details, of previously published results on the quantum stabilization of cosmic strings. Stabilization occurs through the coupling to a heavy fermion doublet in a reduced version of the standard model. We combine the vacuum polarization energy of fermion zero-point fluctuations and the binding energy of occupied energy levels, which are of the same order in a semi-classical expansion. Populating these bound states assigns a charge to the string. We show that strings carrying fermion charge become stable if the electro-weak bosons are coupled to a fermion that is less than twice as heavy as the top quark. The vacuum remains stable in our model, because neutral strings are not energetically favored. These findings suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model.N. GrahamM. QuandtH. Weigel10.1103/PhysRevD.84.02501738 pages, 6 figures, version accepted for publication in Phys Rev DPhys.Rev.D84:025017,2011http://arxiv.org/abs/1103.1911v22011-05-31T13:40:52-04:002011-03-09T17:36:37-05:00Generation of Coherent Structures After Cosmic InflationWe investigate the nonlinear dynamics of hybrid inflation models, which are characterized by two real scalar fields interacting quadratically. We start by solving numerically the coupled Klein-Gordon equations in static Minkowski spacetime, searching for possible coherent structures. We find long-lived, localized configurations, which we identify as a new kind of oscillon. We demonstrate that these two-field oscillons allow for "excited" states with much longer lifetimes than those found in previous studies of single-field oscillons. We then solve the coupled field equations in an expanding Friedmann-Robertson-Walker spacetime, finding that as the field responsible for inflating the Universe rolls down to oscillate about its minimum, it triggers the formation of long-lived two-field oscillons, which can contribute up to 20% of the total energy density of the Universe. We show that these oscillons emerge for a wide range of parameters consistent with WMAP 7-year data. These objects contain total energy of about 25*10^20 GeV, localized in a region of approximate radius 6*10^-26 cm. We argue that these structures could have played a key role during the reheating of the Universe.Marcelo GleiserNoah GrahamNikitas Stamatopoulos10.1103/PhysRevD.83.09601012 pages, 10 .pdf figures, uses RevTex4; v2: expanded discussion in section IV, accepted for publication in Phys.Rev. D. Results remain the samePhys.Rev.D83:096010,2011http://arxiv.org/abs/1103.5942v12011-03-30T10:36:50-04:002011-03-30T10:36:50-04:00Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge GeometriesAn exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the "knife-edge" limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.Noah GrahamAlexander ShpuntThorsten EmigSahand Jamal RahiRobert L. JaffeMehran Kardar10.1103/PhysRevD.83.12500717 pages, 10 figures, uses RevTeX 4Phys.Rev.D83:125007,2011http://arxiv.org/abs/1011.2636v22011-02-24T01:38:30-05:002010-11-11T07:48:09-05:00Stable charged cosmic stringsWe study the quantum stabilization of a cosmic string by a heavy fermion doublet in a reduced version of the standard model. We show that charged strings, obtained by populating fermionic bound state levels, become stable if the electro--weak bosons are coupled to a fermion that is less than twice as heavy as the top quark. This result suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model. Numerically we find the most favorable string profile to be a simple "trough" in the Higgs vev of radius $\approx 10^{-18}\,\mathrm{m}$. The vacuum remains stable in our model, because neutral strings are not energetically favored.H. WeigelM. QuandtN. Graham10.1103/PhysRevLett.106.1016015 pages, 3 figures, version to be published in Phys. Rev. LettPhys.Rev.Lett.106:101601,2011http://arxiv.org/abs/1102.1486v12011-02-07T20:12:32-05:002011-02-07T20:12:32-05:00Electromagnetic Casimir Energies of Semi-Infinite PlanesUsing recently developed techniques based on scattering theory, we find the electromagnetic Casimir energy for geometries involving semi-infinite planes, a case that is of particular interest in the design of microelectromechanical devices. We obtain both approximate analytic formulae and exact results requiring only modest numerical computation. Using these results, we analyze the effects of edges and orientation on the Casimir energy. We also demonstrate the accuracy, simplicity, and utility of our approximation scheme, which is based on a multiple reflection expansion.Mohammad F. MaghrebiNoah Graham10.1209/0295-5075/95/140016 pages, 4 figures, uses RevTeX4Europhys.Lett.95:14001,2011http://arxiv.org/abs/1004.4658v22010-07-26T17:15:46-04:002010-04-26T17:11:59-04:00Long-Lived Time-Dependent Remnants During Cosmological Symmetry Breaking: From Inflation to the Electroweak ScaleThrough a detailed numerical investigation in three spatial dimensions, we demonstrate that long-lived time-dependent field configurations emerge dynamically during symmetry breaking in an expanding de Sitter spacetime. We investigate two situations: a single scalar field with a double-well potential and the bosonic sector of an SU(2) non-Abelian Higgs model. For the single scalar, we show that large-amplitude oscillon configurations emerge spontaneously and persist to contribute about 1.2% of the energy density of the universe. We also show that for a range of parameters, oscillon lifetimes are enhanced by the expansion and that this effect is a result of parametric resonance. For the SU(2) case, we see about 4% of the final energy density in oscillons.Marcelo GleiserNoah GrahamNikitas Stamatopoulos10.1103/PhysRevD.82.04351710 pages, RevTex4, 6 figures; v2: expanded SU(2) model section, added 2 figures, added one section, improved overall presentation and updated references, accepted for publication in Phys. Rev. D. Results remain the samePhys.Rev.D82:043517,2010http://arxiv.org/abs/0910.4649v42010-07-05T23:26:15-04:002009-10-24T09:29:33-04:00Casimir Force at a Knife's EdgeThe Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, $H$ and $\theta$, and the cylinder's parabolic radius $R$. As $H/R\to 0$, the proximity force approximation becomes exact. The opposite limit of $R/H\to 0$ corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.Noah GrahamAlexander ShpuntThorsten EmigSahand Jamal RahiRobert L. JaffeMehran Kardar10.1103/PhysRevD.81.0617015 pages, 3 figures, uses RevTeX; v2: expanded conclusions; v3: fixed missing factor in Eq. (3) and incorrect diagram label (no changes to results); v4: fix similar factor in Eq. (16) (again no changes to results)Phys.Rev.D81:061701,2010http://arxiv.org/abs/0912.3463v22010-01-26T03:59:01-05:002009-12-17T12:11:49-05:00Vacuum Energies of Non--Abelian String--Configurations in 3+1 DimensionsWe develop a method to compute the fermion contribution to the vacuum polarization energy of string--like configurations in a non--abelian gauge theory. This calculation has been hampered previously by a number of technical obstacles. We use gauge invariance of the energy and separation of length scales in the energy density to overcome these obstacles. We present a proof-of-principle investigation that shows that this energy is small in the MS-bar renormalization scheme. The generalization to other schemes is straightforward.H. WeigelM. QuandtN. GrahamO. Schroeder10.1016/j.nuclphysb.2010.01.02021 pages, 5 tables, matches version accepted by Nucl Phys BNucl.Phys.B831:306-328,2010http://arxiv.org/abs/0906.0089v12009-05-30T11:19:23-04:002009-05-30T11:19:23-04:003D scalar model as a 4D perfect conductor limit: dimensional reduction and variational boundary conditionsUnder dimensional reduction, a system in D spacetime dimensions will not necessarily yield its D-1-dimensional analog version. Among other things, this result will depend on the boundary conditions and the dimension D of the system. We investigate this question for scalar and abelian gauge fields under boundary conditions that obey the symmetries of the action. We apply our findings to the Casimir piston, an ideal system for detecting boundary effects. Our investigation is not limited to extra dimensions and we show that the original piston scenario proposed in 2004, a toy model involving a scalar field in 3D (2+1)dimensions, can be obtained via dimensional reduction from a more realistic 4D electromagnetic (EM) system. We show that for perfect conductor conditions, a D-dimensional EM field reduces to a D-1 scalar field and not its lower-dimensional version. For Dirichlet boundary conditions, no theory is recovered under dimensional reduction and the Casimir pressure goes to zero in any dimension. This "zero Dirichlet" result is useful for understanding the EM case. We then identify two special systems where the lower-dimensional version is recovered in any dimension: systems with perfect magnetic conductor (PMC) and Neumann boundary conditions. We show that these two boundary conditions can be obtained from a variational procedure in which the action vanishes outside the bounded region. The fields are free to vary on the surface and have zero modes which survive after dimensional reduction.A. EderyN. GrahamI. MacDonald10.1103/PhysRevD.79.12501814 pages, 2 figuresPhys.Rev.D79:125018,2009http://arxiv.org/abs/0811.1597v12008-11-10T17:27:12-05:002008-11-10T17:27:12-05:00Casimir manipulations: The orientation dependence of fluctuation-induced forcesThe Casimir interaction between two objects, or between an object and a plane, depends on their relative orientations. We make these angular dependences explicit by considering prolate or oblate spheroids. The variation with orientation is calculated exactly at asymptotically large distances for the electromagnetic field, and at arbitrary separations for a scalar field. For a spheroid in front of a mirror, the leading term is orientation independent, and we find the optimal orientation from computations at higher order.T. EmigN. GrahamR. L. JaffeM. Kardar10.1103/PhysRevA.79.0549014 pages, 3 figuresPhys.Rev.A79:054901,2009http://arxiv.org/abs/0712.3034v22008-06-11T19:33:52-04:002007-12-18T14:48:31-05:00Emergence of Oscillons in an Expanding BackgroundWe consider a (1+1) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now lose energy, but at a rate that is exponentially small when the expansion rate is slow. We also show numerically that a universe that starts with (almost) thermal initial conditions will cool to a final state where a significant fraction of the energy of the universe -- on the order of 50% -- is stored in oscillons. If this phenomenon persists in realistic models, oscillons may have cosmological consequences.E. FarhiN. GrahamA. H. GuthN. IqbalR. R. RosalesN. Stamatopoulos10.1103/PhysRevD.77.08501913 pages, 4 .eps figures, uses RevTeX4; v2: clarified details of expansion, added referencesPhys.Rev.D77:085019,2008http://arxiv.org/abs/0706.4125v22007-10-27T20:53:57-04:002007-06-27T20:47:04-04:00Numerical Simulation of an Electroweak OscillonNumerical simulations of the bosonic sector of the $SU(2)\times U(1)$ electroweak Standard Model in 3+1 dimensions have demonstrated the existence of an oscillon -- an extremely long-lived, localized, oscillatory solution to the equations of motion -- when the Higgs mass is equal to twice the $W^\pm$ boson mass. It contains total energy roughly 30 TeV localized in a region of radius 0.05 fm. A detailed description of these numerical results is presented.N. Graham10.1103/PhysRevD.76.08501712 pages, 8 figures, uses RevTeX4; v2: expanded results section, fixed typosPhys.Rev.D76:085017,2007http://arxiv.org/abs/0710.4386v12007-10-24T02:53:44-04:002007-10-24T02:53:44-04:00Quantum stabilization of Z-strings, a status report on D=3+1 dimensionsWe investigate an extension to the phase shift formalism for calculating one-loop determinants. This extension is motivated by requirements of the computation of Z-string quantum energies in D=3+1 dimensions. A subtlety that seems to imply that the vacuum polarization diagram in this formalism is (erroneously) finite is thoroughly investigated.O. SchroederN. GrahamM. QuandtH. Weigel10.1088/1751-8113/41/16/164049Based on talk by O.S. at QFEXT07, Leipzig Sept. 2007. 8 pagesJ.Phys.A41:164049,2008http://arxiv.org/abs/0710.3084v12007-10-16T11:35:49-04:002007-10-16T11:35:49-04:00Casimir Forces between Compact Objects: I. The Scalar CaseWe have developed an exact, general method to compute Casimir interactions between a finite number of compact objects of arbitrary shape and separation. Here, we present details of the method for a scalar field to illustrate our approach in its most simple form; the generalization to electromagnetic fields is outlined in Ref. [1]. The interaction between the objects is attributed to quantum fluctuations of source distributions on their surfaces, which we decompose in terms of multipoles. A functional integral over the effective action of multipoles gives the resulting interaction. Each object's shape and boundary conditions enter the effective action only through its scattering matrix. Their relative positions enter through universal translation matrices that depend only on field type and spatial dimension. The distinction of our method from the pairwise summation of two-body potentials is elucidated in terms of the scattering processes between three objects. To illustrate the power of the technique, we consider Robin boundary conditions $\phi -\lambda \partial_n \phi=0$, which interpolate between Dirichlet and Neumann cases as $\lambda$ is varied. We obtain the interaction between two such spheres analytically in a large separation expansion, and numerically for all separations. The cases of unequal radii and unequal $\lambda$ are studied. We find sign changes in the force as a function of separation in certain ranges of $\lambda$ and see deviations from the proximity force approximation even at short separations, most notably for Neumann boundary conditions.T. EmigN. GrahamR. L. JaffeM. Kardar10.1103/PhysRevD.77.02500527 pages, 9 figuresPhys.Rev.D77:025005,2008http://arxiv.org/abs/0707.1862v22007-09-06T13:36:12-04:002007-07-12T15:09:07-04:00Casimir forces between arbitrary compact objectsWe develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As an example, we obtain this series for two dielectric spheres and the full interaction at all separations for perfectly conducting spheres.T. EmigN. GrahamR. L. JaffeM. Kardar10.1103/PhysRevLett.99.1704034 pages, 1 figurePhys.Rev.Lett.99:170403,2007http://arxiv.org/abs/0705.3193v22007-08-27T14:54:45-04:002007-05-22T11:24:36-04:00Achronal averaged null energy conditionThe averaged null energy condition (ANEC) requires that the integral over a complete null geodesic of the stress-energy tensor projected onto the geodesic tangent vector is never negative. This condition is sufficient to prove many important theorems in general relativity, but it is violated by quantum fields in curved spacetime. However there is a weaker condition, which is free of known violations, requiring only that there is no self-consistent space-time in semiclassical gravity in which ANEC is violated on a complete, {\em achronal} null geodesic. We indicate why such a condition might be expected to hold and show that it is sufficient to rule out wormholes and closed timelike curves.Noah GrahamKen D. Olum10.1103/PhysRevD.76.0640018 pages, RevTeX; v2: qualify conditions on theorem 1, fix typosPhys.Rev.D76:064001,2007http://arxiv.org/abs/hep-th/0610267v62007-06-27T13:33:37-04:002006-10-25T08:22:22-04:00An Electroweak OscillonA recent study demonstrated the existence of oscillons -- extremely long-lived localized configurations that undergo regular oscillations in time -- in spontaneously broken SU(2) gauge theory with a fundamental Higgs particle whose mass is twice the mass of the gauge bosons. This analysis was carried out in a spherically symmetric ansatz invariant under combined spatial and isospin rotations. We extend this result by considering a numerical simulation of the the full bosonic sector of the $SU(2)\times U(1)$ electroweak Standard Model in 3+1 dimensions, with no assumption of rotational symmetry, for a Higgs mass equal to twice the $W^\pm$ boson mass. Within the limits of this numerical simulation, we find that the oscillon solution from the pure SU(2) theory is modified but remains stable in the full electroweak theory. The observed oscillon solution contains total energy approximately 30 TeV localized in a region of radius approximately 0.05 fm.N. Graham10.1103/PhysRevLett.98.101801 10.1103/PhysRevLett.98.1899046 pages, 2 .eps figures, uses revtex4; v2: expanded numerical section, fixed minor errors, various improvements to presentation; v3: fixed typos; v4: fixed typos (most introduced in v2); v5: fixed typo in unit conversion; v6: fix overall scaling factor for energyPhys.Rev.Lett.98:101801,2007; Erratum-ibid.98:189904,2007http://arxiv.org/abs/hep-th/0607092v22006-10-20T12:21:47-04:002006-07-14T03:22:29-04:00Quantum Energies of Strings in a 2+1 Dimensional Gauge TheoryWe study classically unstable string type configurations and compute the renormalized vacuum polarization energies that arise from fermion fluctuations in a 2+1 dimensional analog of the standard model. We then search for a minimum of the total energy (classical plus vacuum polarization energies) by varying the profile functions that characterize the string. We find that typical string configurations bind numerous fermions and that populating these levels is beneficial to further decrease the total energy. Ultimately our goal is to explore the stabilization of string type configurations in the standard model through quantum effects.
We compute the vacuum polarization energy within the phase shift formalism which identifies terms in the Born series for scattering data and Feynman diagrams. This approach allows us to implement standard renormalization conditions of perturbation theory and thus yields the unambiguous result for this non--perturbative contribution to the total energy.N. GrahamM. QuandtO. SchroederH. Weigel10.1016/j.nuclphysb.2006.09.02126 pages, 20 eps-files combined to 8 figures, minor typos corrected. Version to be published in Nucl. Phys. BNucl.Phys.B758:112-143,2006http://arxiv.org/abs/hep-th/0604134v22006-07-11T09:58:57-04:002006-04-19T13:43:08-04:00Unnatural Oscillon Lifetimes in an Expanding BackgroundWe consider a classical toy model of a massive scalar field in 1+1 dimensions with a constant exponential expansion rate of space. The nonlinear theory under consideration supports approximate oscillon solutions, but they eventually decay due to their coupling to the expanding background. Although all the parameters of the theory and the oscillon energies are of order one in units of the scalar field mass $m$, the oscillon lifetime is exponentially large in these natural units. For typical values of the parameters, we see oscillon lifetimes scaling approximately as $\tau \propto \exp(k E/m)/m$ where $E$ is the oscillon energy and the constant $k$ is on the order of 5 to 15 for expansion rates between $H=0.02m$ and $H=0.01m$.N. GrahamN. Stamatopoulos10.1016/j.physletb.2006.06.0707 pages, 2 .eps figures; v2: expanded discussion of decay, fixed typos; version to appear in Physics Letters BPhys.Lett.B639:541-545,2006http://arxiv.org/abs/hep-th/0601038v12006-01-06T11:54:55-05:002006-01-06T11:54:55-05:00Casimir Energies and General Relativity Energy ConditionsQuantum systems often contain negative energy densities. In general relativity, negative energies lead to time advancement, rather than the usual time delay. As a result, some Casimir systems appear to violate energy conditions that would protect against exotic phenomena such as closed timelike curves and superluminal travel. However, when one examines a variety of Casimir systems using self-consistent approximations in quantum field theory, one finds that a particular energy condition is still obeyed, which rules out exotic phenomena. I will discuss the methods and results of these calculations in detail and speculate on their potential implications in general relativity.N. Graham10.1088/0305-4470/39/21/S3710 pages, 7 .eps figures; To appear in the proceedings of QFEXT '05, BarcelonaJ.Phys. A39 (2006) 6423-6432http://arxiv.org/abs/hep-th/0506136v22005-11-07T10:17:36-05:002005-06-16T14:07:15-04:00Plate with a hole obeys the averaged null energy conditionThe negative energy density of Casimir systems appears to violate general relativity energy conditions. However, one cannot test the averaged null energy condition (ANEC) using standard calculations for perfectly reflecting plates, because the null geodesic would have to pass through the plates, where the calculation breaks down. To avoid this problem, we compute the contribution to ANEC for a geodesic that passes through a hole in a single plate. We consider both Dirichlet and Neumann boundary conditions in two and three space dimensions. We use a Babinet's principle argument to reduce the problem to a complementary finite disk correction to the perfect mirror result, which we then compute using scattering theory in elliptical and spheroidal coordinates. In the Dirichlet case, we find that the positive correction due to the hole overwhelms the negative contribution of the infinite plate. In the Neumann case, where the infinite plate gives a positive contribution, the hole contribution is smaller in magnitude, so again ANEC is obeyed. These results can be extended to the case of two plates in the limits of large and small hole radii. This system thus provides another example of a situation where ANEC turns out to be obeyed when one might expect it to be violated.Noah GrahamKen D. Olum10.1103/PhysRevD.72.02501313 pages, 6 .eps figures, uses RevTeX4; v2: added references, minor corrections and clarifications in elliptical and spheroidal function notationPhys.Rev.D72:025013,2005http://arxiv.org/abs/hep-th/0505273v12005-05-31T11:31:12-04:002005-05-31T11:31:12-04:00An Oscillon in the SU(2) Gauged Higgs ModelWe study classical dynamics in the spherical ansatz for the SU(2) gauge and Higgs fields of the electroweak Standard Model in the absence of fermions and the photon. With the Higgs boson mass equal to twice the gauge boson mass, we numerically demonstrate the existence of oscillons, extremely long-lived localized configurations that undergo regular oscillations in time. We have only seen oscillons in this reduced theory when the masses are in a two-to-one ratio. If a similar phenomenon were to persist in the full theory, it would suggest a preferred value for the Higgs mass.E. FarhiN. GrahamV. KhemaniR. MarkovR. Rosales10.1103/PhysRevD.72.1017017 pages, 6 .eps figures, uses revtex4 and epsfigPhys.Rev. D72 (2005) 101701http://arxiv.org/abs/hep-th/0410171v22004-11-25T12:00:44-05:002004-10-15T12:25:06-04:00Quantum QED Flux Tubes in 2+1 and 3+1 DimensionsWe compute energies and energy densities of static electromagnetic flux tubes in three and four spacetime dimensions. Our calculation uses scattering data from the potential induced by the flux tube and imposes standard perturbative renormalization conditions. The calculation is exact to one-loop order, with no additional approximation adopted. We embed the flux tube in a configuration with zero total flux so that we can fully apply standard results from scattering theory. We find that upon choosing the same on-shell renormalization conditions, the functional dependence of the energy and energy density on the parameters of the flux tube is very similar for three and four spacetime dimensions. We compare our exact results to those obtained from the derivative and perturbation expansion approximations, and find good agreement for appropriate parameters of the flux tube. This remedies some puzzles in the prior literature.N. GrahamV. KhemaniM. QuandtO. SchroederH. Weigel10.1016/j.nuclphysb.2004.11.05749 pages, 13 figures, minor changes in wording, accepted for publication in Nucl. Phys. BNucl.Phys. B707 (2005) 233-277http://arxiv.org/abs/gr-qc/0407006v12004-07-01T12:07:37-04:002004-07-01T12:07:37-04:00Energy conditions outside a dielectric ballWe show analytically that the vacuum electromagnetic stress-energy tensor outside a ball with constant dielectric constant and permeability always obeys the weak, null, dominant, and strong energy conditions. There are still no known examples in quantum field theory in which the averaged null energy condition in flat spacetime is violated.Noah GrahamKen D. OlumDelia Schwartz-Perlov10.1103/PhysRevD.70.10501912 pages, RevTex4Phys.Rev. D70 (2004) 105019http://arxiv.org/abs/hep-th/0211244v22003-12-30T11:35:00-05:002002-11-25T11:39:53-05:00Negative Energy Densities in Quantum Field Theory With a Background PotentialWe present a general procedure for calculating one-loop ``Casimir'' energy densities for a scalar field coupled to a fixed potential in renormalized quantum field theory. We implement direct subtraction of counterterms computed precisely in dimensional regularization with a definite renormalization scheme. Our procedure allows us to test quantum field theory energy conditions in the presence of background potentials spherically symmetric in some dimensions and independent of others. We explicitly calculate the energy density for several examples. For a square barrier, we find that the energy is negative and divergent outside the barrier, but there is a compensating divergent positive contribution near the barrier on the inside. We also carry out calculations with exactly solvable $\sech^2$ potentials, which arise in the study of solitons and domain walls.Noah GrahamKen D. Olum10.1103/PhysRevD.67.085014 10.1103/PhysRevD.69.10990124 pages, 2 .eps figures; v2: updated with note added in journal, fixed typos, updated referencesPhys.Rev.D67:085014,2003; Erratum-ibid.D69:109901,2004http://arxiv.org/abs/hep-th/0309130v12003-09-12T15:35:36-04:002003-09-12T15:35:36-04:00The Dirichlet Casimir ProblemCasimir forces are conventionally computed by analyzing the effects of boundary conditions on a fluctuating quantum field. Although this analysis provides a clean and calculationally tractable idealization, it does not always accurately capture the characteristics of real materials, which cannot constrain the modes of the fluctuating field at all energies. We study the vacuum polarization energy of renormalizable, continuum quantum field theory in the presence of a background field, designed to impose a Dirichlet boundary condition in a particular limit. We show that in two and three space dimensions, as a background field becomes concentrated on the surface on which the Dirichlet boundary condition would eventually hold, the Casimir energy diverges. This result implies that the energy depends in detail on the properties of the material, which are not captured by the idealized boundary conditions. This divergence does not affect the force between rigid bodies, but it does invalidate calculations of Casimir stresses based on idealized boundary conditions.N. GrahamR. L. JaffeV. KhemaniM. QuandtO. SchroederH. Weigel10.1016/j.nuclphysb.2003.11.00129 pages, 4 figuresNucl.Phys.B677:379-404,2004http://arxiv.org/abs/hep-th/9805150v32003-07-31T16:53:55-04:001998-05-22T15:37:48-04:00Unambiguous one-loop quantum energies of 1+1 dimensional bosonic field configurationsWe calculate one-loop quantum energies in a renormalizable self-interacting theory in one spatial dimension by summing the zero-point energies of small oscillations around a classical field configuration, which need not be a solution of the classical field equations. We unambiguously implement standard perturbative renormalization using phase shifts and the Born approximation. We illustrate our method by calculating the quantum energy of a soliton/antisoliton pair as a function of their separation. This energy includes an imaginary part that gives a quantum decay rate and is associated with a level crossing in the solutions to the classical field equation in the presence of the source that maintains the soliton/antisoliton pair.N. GrahamR. L. Jaffe10.1016/S0370-2693(98)00795-3Email correspondence to graham@mitlns.mit.edu ; 10 pages, 2 figures, REVTeX, BoxedEPS; v2: Fixed description of level crossing as a function of $x_0$; v3: Fixed numerical error in figure dataPhys.Lett. B435 (1998) 145-151http://arxiv.org/abs/hep-th/9901023v22003-07-17T11:11:22-04:001999-01-06T14:42:24-05:00Fermionic One-Loop Corrections to Soliton Energies in 1+1 DimensionsWe demonstrate an unambiguous and robust method for computing fermionic corrections to the energies of classical background field configurations. We consider the particular case of a sequence of background field configurations that interpolates continuously between the trivial vacuum and a widely separated soliton/antisoliton pair in 1+1 dimensions. Working in the continuum, we use phase shifts, the Born approximation, and Levinson's theorem to avoid ambiguities of renormalization procedure and boundary conditions. We carry out the calculation analytically at both ends of the interpolation and numerically in between, and show how the relevant physical quantities vary continuously. In the process, we elucidate properties of the fermionic phase shifts and zero modes.N. GrahamR. L. Jaffe10.1016/S0550-3213(99)00148-012 pages, 4 figures, uses BoxedEPS;v2: fixed numerical error in figure dataNucl.Phys. B549 (1999) 516-526http://arxiv.org/abs/hep-th/0303159v12003-03-18T12:26:03-05:002003-03-18T12:26:03-05:00Heavy Fermion Quantum Effects in SU(2)_L Gauge TheoryWe explore the effects of a heavy fermion doublet in a simplified version of the standard electroweak theory. We integrate out the doublet and compute the exact effective energy functional of spatially varying gauge and Higgs fields. We perform a variational search for a local minimum of the effective energy and do not find evidence for a soliton carrying the quantum numbers of the decoupled fermion doublet. The fermion vacuum polarization energy offsets the gain in binding energy previously argued to be sufficient to stabilize a fermionic soliton. The existence of such a soliton would have been a natural way to maintain anomaly cancellation at the level of the states. We also see that the sphaleron energy is significantly increased due to the quantum corrections of the heavy doublet. We find that when the doublet is slightly heavier than the quantum--corrected sphaleron, its decay is exponentially suppressed owing to a new barrier. This barrier exists only for an intermediate range of fermion masses, and a heavy enough doublet is indeed unstable.E. FarhiN. GrahamR. L. JaffeV. KhemaniH. Weigel10.1016/S0550-3213(03)00487-530 pages LaTeX, 3 eps-figuresNucl.Phys. B665 (2003) 623-648http://arxiv.org/abs/hep-th/0207205v32003-01-30T04:37:09-05:002002-07-23T08:47:06-04:00Casimir Energies in Light of Quantum Field TheoryWe study the Casimir problem as the limit of a conventional quantum field theory coupled to a smooth background. The Casimir energy diverges in the limit that the background forces the field to vanish on a surface. We show that this divergence cannot be absorbed into a renormalization of the parameters of the theory. As a result, the Casimir energy of the surface and other quantities like the surface tension, which are obtained by deforming the surface, cannot be defined independently of the details of the coupling between the field and the matter on the surface. In contrast, the energy density away from the surface and the force between rigid surfaces are finite and independent of these complications.N. GrahamR. L. JaffeV. KhemaniM. QuandtM. ScandurraH. Weigel10.1016/j.physletb.2003.03.0035pages, REVTeX, no figures., Modifications to emphasize novel aspects of workPhys.Lett.B572:196-201,2003http://arxiv.org/abs/hep-th/0207120v22002-07-12T21:35:30-04:002002-07-12T12:43:50-04:00Calculating Vacuum Energies in Renormalizable Quantum Field Theories: A New Approach to the Casimir ProblemThe Casimir problem is usually posed as the response of a fluctuating quantum field to externally imposed boundary conditions. In reality, however, no interaction is strong enough to enforce a boundary condition on all frequencies of a fluctuating field. We construct a more physical model of the situation by coupling the fluctuating field to a smooth background potential that implements the boundary condition in a certain limit. To study this problem, we develop general new methods to compute renormalized one--loop quantum energies and energy densities. We use analytic properties of scattering data to compute Green's functions in time--independent background fields at imaginary momenta. Our calculational method is particularly useful for numerical studies of singular limits because it avoids terms that oscillate or require cancellation of exponentially growing and decaying factors. To renormalize, we identify potentially divergent contributions to the Casimir energy with low orders in the Born series to the Green's function. We subtract these contributions and add back the corresponding Feynman diagrams, which we combine with counterterms fixed by imposing standard renormalization conditions on low--order Green's functions. The resulting Casimir energy and energy density are finite functionals for smooth background potentials. In general, however, the Casimir energy diverges in the boundary condition limit. This divergence is real and reflects the infinite energy needed to constrain a fluctuating field on all energy scales; renormalizable quantum field theories have no place for ad hoc surface counterterms. We apply our methods to simple examples to illustrate cases where these subtleties invalidate the conclusions of the boundary condition approach.N. GrahamR. L. JaffeV. KhemaniM. QuandtM. ScandurraH. Weigel10.1016/S0550-3213(02)00823-436pages, Latex, 20 eps files. included via epsfigNucl.Phys. B645 (2002) 49-84http://arxiv.org/abs/gr-qc/0205134v32002-12-07T12:25:31-05:002002-05-30T21:18:02-04:00Static Negative Energies Near a Domain WallWe show that a system of a domain wall coupled to a scalar field has static negative energy density at certain distances from the domain wall. This system provides a simple, explicit example of violation of the averaged weak energy condition and the quantum inequalities by interacting quantum fields. Unlike idealized systems with boundary conditions or external background fields, this calculation is implemented precisely in renormalized quantum field theory with the energy necessary to support the background field included self-consistently.Ken D. OlumNoah Graham10.1016/S0370-2693(03)00011-X6 pages, 1 figure, uses RevTeX4; v2: added acknowledgements; v3: minor correction and clarificationsPhys.Lett. B554 (2003) 175-179http://arxiv.org/abs/hep-th/0205257v12002-05-24T13:55:15-04:002002-05-24T13:55:15-04:00Sphalerons, knots, and dynamical compactification in Yang-Mills-Chern-Simon theoriesEuclidean d=3 SU(2) Yang-Mills-Chern-Simons (YMCS) theory, including Georgi-Glashow (GGCS) theory, may have solitons in the presence of appropriate mass terms. For integral CS level k and for solitons carrying integral CS number, YMCS is gauge-invariant and consistent. However, individual solitons such as sphalerons and linked center vortices with CS number of 1/2 and writhing center vortices with arbitrary CS number are non-compact; a condensate of them threatens compactness of the theory. We study various forms of the non-compact theory in the dilute-gas approximation, treating the parameters of non-compact large gauge transformations as collective coordinates. We conclude: 1) YMCS theory dynamically compactifies; non-compact YMCS have infinitely higher vacuum energy than compact YMCS. 2) An odd number of sphalerons is associated with a domain- wall sphaleron, a pure-gauge configuration on a closed surface enclosing them and with a half-integral CS number. 3) We interpret the domain-wall sphaleron in terms of fictitious closed Abelian magnetic field lines that express the links of the Hopf fibration. Sphalerons are over- and under-crossings of knots in the field lines; the domain-wall sphaleron is a superconducting wall confining these knots to a compact domain. 4) Analogous results hold for center vortices and nexuses. 5) For a CS term induced with an odd number of fermion doublets, domain-wall sphalerons are related to non-normalizable fermion modes. 6) GGCS with monopoles is compactified with center-vortex-like strings.John M. CornwallNoah Graham10.1103/PhysRevD.66.065012RevTeX4; 27 pages, including 5 .eps figuresPhys.Rev.D66:065012,2002http://arxiv.org/abs/hep-th/0201148v12002-01-18T14:39:09-05:002002-01-18T14:39:09-05:00Casimir Effects in Renormalizable Quantum Field TheoriesWe review the framework we and our collaborators have developed for the study of one-loop quantum corrections to extended field configurations in renormalizable quantum field theories. We work in the continuum, transforming the standard Casimir sum over modes into a sum over bound states and an integral over scattering states weighted by the density of states. We express the density of states in terms of phase shifts, allowing us to extract divergences by identifying Born approximations to the phase shifts with low order Feynman diagrams. Once isolated in Feynman diagrams, the divergences are canceled against standard counterterms. Thus regulated, the Casimir sum is highly convergent and amenable to numerical computation. Our methods have numerous applications to the theory of solitons, membranes, and quantum field theories in strong external fields or subject to boundary conditions.Noah GrahamRobert L. JaffeHerbert Weigel10.1142/S0217751X0201022427 pp., 11 EPS figures, LaTeX using ijmpa1.sty; email correspondence to R.L. Jaffe <jaffe@mit.edu> ; based on talks presented by the authors at the 5th workshop `QFTEX', Leipzig, September 2001Int.J.Mod.Phys. A17 (2002) 846-869http://arxiv.org/abs/hep-th/0112217v12001-12-21T15:00:26-05:002001-12-21T15:00:26-05:00Searching for Quantum Solitons in a 3+1 Dimensional Chiral Yukawa ModelWe search for static solitons stabilized by heavy fermions in a 3+1 dimensional Yukawa model. We compute the renormalized energy functional, including the exact one-loop quantum corrections, and perform a variational search for configurations that minimize the energy for a fixed fermion number. We compute the quantum corrections using a phase shift parameterization, in which we renormalize by identifying orders of the Born series with corresponding Feynman diagrams. For higher-order terms in the Born series, we develop a simplified calculational method. When applicable, we use the derivative expansion to check our results. We observe marginally bound configurations at large Yukawa coupling, and discuss their interpretation as soliton solutions subject to general limitations of the model.E. FarhiN. GrahamR. L. JaffeH. Weigel10.1016/S0550-3213(02)00172-427 pp., 7 EPS files; email correspondence to jaffe@mit.eduNucl.Phys. B630 (2002) 241-268http://arxiv.org/abs/hep-th/0112148v22001-12-18T16:53:23-05:002001-12-17T15:35:25-05:00Exact One-Loop Thermal Free Energies of SolitonsI show how to compute the exact one-loop thermal correction to the free energy of a soliton. The method uses the effective potential as an auxiliary step to ensure that the soliton is quantized around the appropriate vacuum. The exact result is then computed using scattering theory techniques, and includes all orders in the derivative expansion. It can be efficiently combined with a calculation of the exact quantum correction to yield the full free energy to one loop. I demonstrate this technique with explicit computations in $\phi^4$ models, obtaining the free energy for a kink in 1+1 dimensions and a domain wall in 2+1 dimensions.N. Graham10.1016/S0370-2693(02)01244-38 pages, 4 figures, uses RevTeX4; v2 fixed formatting (no changes to text)Phys.Lett. B529 (2002) 178-185http://arxiv.org/abs/hep-th/0103010v22001-08-23T03:31:31-04:002001-03-01T18:47:32-05:00Quantum Energies of InterfacesWe present a method for computing the one-loop, renormalized quantum energies of symmetrical interfaces of arbitrary dimension and codimension using elementary scattering data. Internal consistency requires finite-energy sum rules relating phase shifts to bound state energies.N. GrahamR. L. JaffeM. QuandtH. Weigel10.1103/PhysRevLett.87.1316018 pages, 1 figure, minor changes, Phys. Rev. Lett., in printPhys.Rev.Lett. 87 (2001) 131601http://arxiv.org/abs/hep-th/0105009v22001-05-14T02:08:48-04:002001-05-02T03:09:18-04:00Quantum Corrections to Q-BallsWe extend calculational techniques for static solitons to the case of field configurations with simple time dependence in order to consider quantum effects on the stability of Q-balls. These nontopological solitons exist classically for any fixed value of an unbroken global charge Q. We show that one-loop quantum effects can destabilize very small Q-balls. We show how the properties of the soliton are reflected in the associated scattering problem, and find that a good approximation to the full one-loop quantum energy of a Q-ball is given by $\omega - E_0$, where $\omega$ is the frequency of the classical soliton's time dependence, and $E_0$ is the energy of the lowest bound state in the associated scattering problem.N. Graham10.1016/S0370-2693(01)00669-46 pages, 2 figures, uses RevTex4; v2: replaced figuresPhys.Lett. B513 (2001) 112-118http://arxiv.org/abs/quant-ph/0104136v12001-04-28T19:30:00-04:002001-04-28T19:30:00-04:00Finite Energy Sum Rules in Potential ScatteringWe study scattering theory identities previously obtained as consistency conditions in the context of one-loop quantum field theory calculations. We prove the identities using Jost function techniques and study applications.N. GrahamR. L. JaffeM. QuandtH. Weigel10.1006/aphy.2001.617315 pages, 1 figure, uses RevTex4Annals Phys. 293 (2001) 240http://arxiv.org/abs/hep-th/0007189v22000-12-06T13:51:08-05:002000-07-24T14:54:06-04:00Fractional and Integer Charges from Levinson's TheoremWe compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a 1+1 dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions.E. FarhiN. GrahamR. L. JaffeH. Weigel10.1016/S0550-3213(00)00665-916 pages, uses RevTex, 1 figure; v2: minor correctionsNucl.Phys. B595 (2001) 536-550http://arxiv.org/abs/hep-th/0003144v32000-07-06T14:33:07-04:002000-03-16T13:10:21-05:00Heavy Fermion Stabilization of Solitons in 1+1 DimensionsWe find static solitons stabilized by quantum corrections in a (1+1)-dimensional model with a scalar field chirally coupled to fermions. This model does not support classical solitons. We compute the renormalized energy functional including one-loop quantum corrections. We carry out a variational search for a configuration that minimizes the energy functional. We find a nontrivial configuration with fermion number whose energy is lower than the same number of free fermions quantized about the translationally invariant vacuum. In order to compute the quantum corrections for a given background field we use a phase-shift parameterization of the Casimir energy. We identify orders of the Born series for the phase shift with perturbative Feynman diagrams in order to renormalize the Casimir energy using perturbatively determined counterterms. Generalizing dimensional regularization, we demonstrate that this procedure yields a finite and unambiguous energy functional.E. FarhiN. GrahamR. L. JaffeH. Weigel10.1016/S0550-3213(00)00371-027 papes Latex, equation labels corrected, version to be published in Nucl. Phys. BNucl.Phys. B585 (2000) 443http://arxiv.org/abs/hep-th/9808140v52000-04-07T11:20:01-04:001998-08-21T17:07:35-04:00Energy, Central Charge, and the BPS Bound for 1+1 Dimensional Supersymmetric SolitonsWe consider one-loop quantum corrections to soliton energies and central charges in the supersymmetric $\phi^4$ and sine-Gordon models in 1+1 dimensions. In both models, we unambiguously calculate the correction to the energy in a simple renormalization scheme and obtain $\Delta H = - m/(2\pi)$, in agreement with previous results. Furthermore, we show that there is an identical correction to the central charge, so that the BPS bound remains saturated in the one-loop approximation. We extend these results to arbitrary 1+1 dimensional supersymmetric theories.N. GrahamR. L. Jaffe10.1016/S0550-3213(99)00027-915 pages, RevTeX; v2: generalized energy result, added minor clarifications, and fixed typos; v3: more minor clarifications and corrections; v4: fixed factor of 2 in eq. (25); v5: fixed minor error in eq. (55)Nucl.Phys. B544 (1999) 432-447http://arxiv.org/abs/hep-th/9912283v32000-03-27T13:05:07-05:001999-12-30T18:58:18-05:00A Heavy Fermion Can Create a Soliton: A 1+1 Dimensional ExampleWe show that quantum effects can stabilize a soliton in a model with no soliton at the classical level. The model has a scalar field chirally coupled to a fermion in 1+1 dimensions. We use a formalism that allows us to calculate the exact one loop fermion contribution to the effective energy for a spatially varying scalar background. This energy includes the contribution from counterterms fixed in the perturbative sector of the theory. The resulting energy is therefore finite and unambiguous. A variational search then yields a fermion number one configuration whose energy is below that of a single free fermion.E. FarhiN. GrahamR. L. JaffeH. Weigel10.1016/S0370-2693(00)00108-810 pages, RevTeX, 2 figures composed from 4 .eps files; v2: fixed minor errors, added reference; v3: corrected reference added in v2Phys.Lett. B475 (2000) 335http://arxiv.org/abs/hep-th/9912286v32000-04-07T11:14:13-04:001999-12-30T19:20:15-05:00Exact Renormalized One-Loop Quantum Corrections to Energies of Solitonic Field ConfigurationsWe develop a method for computing exact one-loop quantum corrections to the energies of static classical backgrounds in renormalizable quantum field theories. We use a continuum density of states formalism to construct a regularized Casimir energy in terms of phase shifts and their Born approximations. This method unambiguously incorporates definite counterterms fixed in the standard way by physical renormalization conditions. The result is a robust computation that can be efficiently implemented both numerically and analytically. We carry out such calculations in models of bosons and fermions in one and three dimensions.N. GrahamM.I.T. Ph.D thesis; 72 pages, uses mitthesis.sty; v2: fixed minor error in eq (B.22); v3: fixed minor error in eq. (4.57)http://arxiv.org/abs/hep-th/9802015v11998-02-03T14:59:02-05:001998-02-03T14:59:02-05:00Finite Quantum Fluctuations About Static Field ConfigurationsWe develop an unambiguous and practical method to calculate one-loop quantum corrections to the energies of classical time-independent field configurations in renormalizable field theories. We show that the standard perturbative renormalization procedure suffices here as well. We apply our method to a simplified model where a charged scalar couples to a neutral "Higgs" field, and compare our results to the derivative expansion.Edward FarhiNoah GrahamPeter E. HaagensenRobert L. Jaffe10.1016/S0370-2693(98)00354-216 pp. LaTeX, 3 figs., BoxedEPSPhys.Lett. B427 (1998) 334-342